Properties

Label 2001.1.bf.c.275.2
Level $2001$
Weight $1$
Character 2001.275
Analytic conductor $0.999$
Analytic rank $0$
Dimension $24$
Projective image $D_{84}$
CM discriminant -23
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2001.bf (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.998629090279\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(2\) over \(\Q(\zeta_{28})\)
Coefficient field: \(\Q(\zeta_{84})\)
Defining polynomial: \(x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{84}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{84} - \cdots)\)

Embedding invariants

Embedding label 275.2
Root \(-0.680173 + 0.733052i\) of defining polynomial
Character \(\chi\) \(=\) 2001.275
Dual form 2001.1.bf.c.1448.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.59908 - 0.180173i) q^{2} +(0.826239 + 0.563320i) q^{3} +(1.54966 - 0.353699i) q^{4} +(1.42271 + 0.751927i) q^{6} +(0.895403 - 0.313315i) q^{8} +(0.365341 + 0.930874i) q^{9} +O(q^{10})\) \(q+(1.59908 - 0.180173i) q^{2} +(0.826239 + 0.563320i) q^{3} +(1.54966 - 0.353699i) q^{4} +(1.42271 + 0.751927i) q^{6} +(0.895403 - 0.313315i) q^{8} +(0.365341 + 0.930874i) q^{9} +(1.47963 + 0.580713i) q^{12} +(-0.858075 - 1.78181i) q^{13} +(-0.0567315 + 0.0273204i) q^{16} +(0.751927 + 1.42271i) q^{18} +(-0.781831 + 0.623490i) q^{23} +(0.916313 + 0.245525i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(-1.69316 - 2.69465i) q^{26} +(-0.222521 + 0.974928i) q^{27} +(0.680173 + 0.733052i) q^{29} +(0.0579571 + 0.514383i) q^{31} +(-0.889030 + 0.558615i) q^{32} +(0.895403 + 1.31332i) q^{36} +(0.294755 - 1.95557i) q^{39} +(-0.922474 + 0.922474i) q^{41} +(-1.13787 + 1.13787i) q^{46} +(-0.0246991 + 0.0705858i) q^{47} +(-0.0622639 - 0.00938477i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(-0.531484 - 1.51889i) q^{50} +(-1.95995 - 2.45770i) q^{52} +(-0.180173 + 1.59908i) q^{54} +(1.21972 + 1.04966i) q^{58} +0.445042i q^{59} +(0.185356 + 0.812096i) q^{62} +(-1.27175 + 1.01419i) q^{64} +(-0.997204 + 0.0747301i) q^{69} +(1.67738 - 0.807782i) q^{71} +(0.618784 + 0.719040i) q^{72} +(0.197979 - 1.75711i) q^{73} +(0.365341 - 0.930874i) q^{75} +(0.118995 - 3.18022i) q^{78} +(-0.733052 + 0.680173i) q^{81} +(-1.30890 + 1.64131i) q^{82} +(0.149042 + 0.988831i) q^{87} +(-0.991043 + 1.24273i) q^{92} +(-0.241876 + 0.457652i) q^{93} +(-0.0267781 + 0.117322i) q^{94} +(-1.04923 - 0.0392594i) q^{96} +(-1.51889 - 0.531484i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{2} + 2q^{3} + 14q^{4} - 2q^{6} + 6q^{8} + 2q^{9} + O(q^{10}) \) \( 24q - 2q^{2} + 2q^{3} + 14q^{4} - 2q^{6} + 6q^{8} + 2q^{9} - 6q^{12} - 6q^{16} + 4q^{18} - 6q^{24} - 4q^{25} + 2q^{26} - 4q^{27} - 2q^{31} + 4q^{32} + 6q^{36} + 2q^{41} + 2q^{46} - 2q^{47} - 4q^{48} - 4q^{49} - 2q^{50} - 10q^{52} + 12q^{54} + 4q^{58} + 4q^{62} - 28q^{64} + 14q^{72} - 2q^{73} + 2q^{75} + 10q^{78} + 2q^{81} - 4q^{82} + 4q^{92} - 2q^{93} - 8q^{94} - 24q^{96} - 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times\).

\(n\) \(553\) \(668\) \(1132\)
\(\chi(n)\) \(e\left(\frac{13}{28}\right)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.59908 0.180173i 1.59908 0.180173i 0.733052 0.680173i \(-0.238095\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(3\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(4\) 1.54966 0.353699i 1.54966 0.353699i
\(5\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(6\) 1.42271 + 0.751927i 1.42271 + 0.751927i
\(7\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(8\) 0.895403 0.313315i 0.895403 0.313315i
\(9\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(10\) 0 0
\(11\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(12\) 1.47963 + 0.580713i 1.47963 + 0.580713i
\(13\) −0.858075 1.78181i −0.858075 1.78181i −0.563320 0.826239i \(-0.690476\pi\)
−0.294755 0.955573i \(-0.595238\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.0567315 + 0.0273204i −0.0567315 + 0.0273204i
\(17\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(18\) 0.751927 + 1.42271i 0.751927 + 1.42271i
\(19\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(24\) 0.916313 + 0.245525i 0.916313 + 0.245525i
\(25\) −0.222521 0.974928i −0.222521 0.974928i
\(26\) −1.69316 2.69465i −1.69316 2.69465i
\(27\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(28\) 0 0
\(29\) 0.680173 + 0.733052i 0.680173 + 0.733052i
\(30\) 0 0
\(31\) 0.0579571 + 0.514383i 0.0579571 + 0.514383i 0.988831 + 0.149042i \(0.0476190\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(32\) −0.889030 + 0.558615i −0.889030 + 0.558615i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.895403 + 1.31332i 0.895403 + 1.31332i
\(37\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(38\) 0 0
\(39\) 0.294755 1.95557i 0.294755 1.95557i
\(40\) 0 0
\(41\) −0.922474 + 0.922474i −0.922474 + 0.922474i −0.997204 0.0747301i \(-0.976190\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(42\) 0 0
\(43\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −1.13787 + 1.13787i −1.13787 + 1.13787i
\(47\) −0.0246991 + 0.0705858i −0.0246991 + 0.0705858i −0.955573 0.294755i \(-0.904762\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(48\) −0.0622639 0.00938477i −0.0622639 0.00938477i
\(49\) −0.900969 0.433884i −0.900969 0.433884i
\(50\) −0.531484 1.51889i −0.531484 1.51889i
\(51\) 0 0
\(52\) −1.95995 2.45770i −1.95995 2.45770i
\(53\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(54\) −0.180173 + 1.59908i −0.180173 + 1.59908i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 1.21972 + 1.04966i 1.21972 + 1.04966i
\(59\) 0.445042i 0.445042i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(60\) 0 0
\(61\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(62\) 0.185356 + 0.812096i 0.185356 + 0.812096i
\(63\) 0 0
\(64\) −1.27175 + 1.01419i −1.27175 + 1.01419i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(68\) 0 0
\(69\) −0.997204 + 0.0747301i −0.997204 + 0.0747301i
\(70\) 0 0
\(71\) 1.67738 0.807782i 1.67738 0.807782i 0.680173 0.733052i \(-0.261905\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(72\) 0.618784 + 0.719040i 0.618784 + 0.719040i
\(73\) 0.197979 1.75711i 0.197979 1.75711i −0.365341 0.930874i \(-0.619048\pi\)
0.563320 0.826239i \(-0.309524\pi\)
\(74\) 0 0
\(75\) 0.365341 0.930874i 0.365341 0.930874i
\(76\) 0 0
\(77\) 0 0
\(78\) 0.118995 3.18022i 0.118995 3.18022i
\(79\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(80\) 0 0
\(81\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(82\) −1.30890 + 1.64131i −1.30890 + 1.64131i
\(83\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0.149042 + 0.988831i 0.149042 + 0.988831i
\(88\) 0 0
\(89\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.991043 + 1.24273i −0.991043 + 1.24273i
\(93\) −0.241876 + 0.457652i −0.241876 + 0.457652i
\(94\) −0.0267781 + 0.117322i −0.0267781 + 0.117322i
\(95\) 0 0
\(96\) −1.04923 0.0392594i −1.04923 0.0392594i
\(97\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(98\) −1.51889 0.531484i −1.51889 0.531484i
\(99\) 0 0
\(100\) −0.689663 1.43210i −0.689663 1.43210i
\(101\) 0.189606 1.68280i 0.189606 1.68280i −0.433884 0.900969i \(-0.642857\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(102\) 0 0
\(103\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(104\) −1.32659 1.32659i −1.32659 1.32659i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(108\) 1.58951i 1.58951i
\(109\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 1.31332 + 0.895403i 1.31332 + 0.895403i
\(117\) 1.34515 1.44973i 1.34515 1.44973i
\(118\) 0.0801844 + 0.711656i 0.0801844 + 0.711656i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(122\) 0 0
\(123\) −1.28183 + 0.242536i −1.28183 + 0.242536i
\(124\) 0.271751 + 0.776619i 0.271751 + 0.776619i
\(125\) 0 0
\(126\) 0 0
\(127\) 0.649042 1.85486i 0.649042 1.85486i 0.149042 0.988831i \(-0.452381\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(128\) −1.10846 + 1.10846i −1.10846 + 1.10846i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.18017 0.132974i −1.18017 0.132974i −0.500000 0.866025i \(-0.666667\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(138\) −1.58114 + 0.299168i −1.58114 + 0.299168i
\(139\) 1.16078 + 1.45557i 1.16078 + 1.45557i 0.866025 + 0.500000i \(0.166667\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(140\) 0 0
\(141\) −0.0601697 + 0.0444073i −0.0601697 + 0.0444073i
\(142\) 2.53671 1.59392i 2.53671 1.59392i
\(143\) 0 0
\(144\) −0.0461582 0.0428286i −0.0461582 0.0428286i
\(145\) 0 0
\(146\) 2.84543i 2.84543i
\(147\) −0.500000 0.866025i −0.500000 0.866025i
\(148\) 0 0
\(149\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(150\) 0.416490 1.55436i 0.416490 1.55436i
\(151\) 0.781831 0.623490i 0.781831 0.623490i −0.149042 0.988831i \(-0.547619\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.234915 3.13472i −0.234915 3.13472i
\(157\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −1.04966 + 1.21972i −1.04966 + 1.21972i
\(163\) 0.0705858 + 0.0246991i 0.0705858 + 0.0246991i 0.365341 0.930874i \(-0.380952\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(164\) −1.10324 + 1.75580i −1.10324 + 1.75580i
\(165\) 0 0
\(166\) 0 0
\(167\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(168\) 0 0
\(169\) −1.81507 + 2.27603i −1.81507 + 2.27603i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(174\) 0.416490 + 1.55436i 0.416490 + 1.55436i
\(175\) 0 0
\(176\) 0 0
\(177\) −0.250701 + 0.367711i −0.250701 + 0.367711i
\(178\) 0 0
\(179\) −1.03030 + 1.29196i −1.03030 + 1.29196i −0.0747301 + 0.997204i \(0.523810\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(180\) 0 0
\(181\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.504706 + 0.803234i −0.504706 + 0.803234i
\(185\) 0 0
\(186\) −0.304322 + 0.775400i −0.304322 + 0.775400i
\(187\) 0 0
\(188\) −0.0133089 + 0.118120i −0.0133089 + 0.118120i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(192\) −1.62208 + 0.121558i −1.62208 + 0.121558i
\(193\) 0.791295 + 0.497204i 0.791295 + 0.497204i 0.866025 0.500000i \(-0.166667\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −1.54966 0.353699i −1.54966 0.353699i
\(197\) −1.35417 + 1.07992i −1.35417 + 1.07992i −0.365341 + 0.930874i \(0.619048\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(198\) 0 0
\(199\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(200\) −0.504706 0.803234i −0.504706 0.803234i
\(201\) 0 0
\(202\) 2.72509i 2.72509i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.866025 0.500000i −0.866025 0.500000i
\(208\) 0.0973598 + 0.0776418i 0.0973598 + 0.0776418i
\(209\) 0 0
\(210\) 0 0
\(211\) 0.467085 + 1.33485i 0.467085 + 1.33485i 0.900969 + 0.433884i \(0.142857\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(212\) 0 0
\(213\) 1.84095 + 0.277479i 1.84095 + 0.277479i
\(214\) 0 0
\(215\) 0 0
\(216\) 0.106214 + 0.942673i 0.106214 + 0.942673i
\(217\) 0 0
\(218\) 0 0
\(219\) 1.15339 1.34027i 1.15339 1.34027i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.62349 0.781831i −1.62349 0.781831i −0.623490 0.781831i \(-0.714286\pi\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0.826239 0.563320i 0.826239 0.563320i
\(226\) 0 0
\(227\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(228\) 0 0
\(229\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.838705 + 0.443269i 0.838705 + 0.443269i
\(233\) 0.149460i 0.149460i 0.997204 + 0.0747301i \(0.0238095\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(234\) 1.88980 2.56059i 1.88980 2.56059i
\(235\) 0 0
\(236\) 0.157411 + 0.689663i 0.157411 + 0.689663i
\(237\) 0 0
\(238\) 0 0
\(239\) 1.94440 + 0.443797i 1.94440 + 0.443797i 0.988831 + 0.149042i \(0.0476190\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(240\) 0 0
\(241\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(242\) 1.36254 + 0.856144i 1.36254 + 0.856144i
\(243\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(244\) 0 0
\(245\) 0 0
\(246\) −2.00605 + 0.618784i −2.00605 + 0.618784i
\(247\) 0 0
\(248\) 0.213059 + 0.442422i 0.213059 + 0.442422i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0.703674 3.08300i 0.703674 3.08300i
\(255\) 0 0
\(256\) −0.558615 + 0.700480i −0.558615 + 0.700480i
\(257\) −1.32624 + 0.302705i −1.32624 + 0.302705i −0.826239 0.563320i \(-0.809524\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(262\) −1.91115 −1.91115
\(263\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.85486 0.649042i 1.85486 0.649042i 0.866025 0.500000i \(-0.166667\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(270\) 0 0
\(271\) 1.05737 1.68280i 1.05737 1.68280i 0.433884 0.900969i \(-0.357143\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −1.51889 + 0.468516i −1.51889 + 0.468516i
\(277\) −0.658322 + 0.317031i −0.658322 + 0.317031i −0.733052 0.680173i \(-0.761905\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(278\) 2.11843 + 2.11843i 2.11843 + 2.11843i
\(279\) −0.457652 + 0.241876i −0.457652 + 0.241876i
\(280\) 0 0
\(281\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(282\) −0.0882151 + 0.0818516i −0.0882151 + 0.0818516i
\(283\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(284\) 2.31365 1.84507i 2.31365 1.84507i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.844799 0.623490i −0.844799 0.623490i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) −0.314690 2.79295i −0.314690 2.79295i
\(293\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(294\) −0.955573 1.29476i −0.955573 1.29476i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.78181 + 0.858075i 1.78181 + 0.858075i
\(300\) 0.236904 1.57176i 0.236904 1.57176i
\(301\) 0 0
\(302\) 1.13787 1.13787i 1.13787 1.13787i
\(303\) 1.10462 1.28359i 1.10462 1.28359i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −0.752407 + 0.752407i −0.752407 + 0.752407i −0.974928 0.222521i \(-0.928571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −0.605443 1.73026i −0.605443 1.73026i −0.680173 0.733052i \(-0.738095\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(312\) −0.348786 1.84338i −0.348786 1.84338i
\(313\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −0.0250721 0.222521i −0.0250721 0.222521i 0.974928 0.222521i \(-0.0714286\pi\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.895403 + 1.31332i −0.895403 + 1.31332i
\(325\) −1.54620 + 1.23305i −1.54620 + 1.23305i
\(326\) 0.117322 + 0.0267781i 0.117322 + 0.0267781i
\(327\) 0 0
\(328\) −0.536961 + 1.11501i −0.536961 + 1.11501i
\(329\) 0 0
\(330\) 0 0
\(331\) 0.262919 + 0.262919i 0.262919 + 0.262919i 0.826239 0.563320i \(-0.190476\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −0.224672 + 1.99402i −0.224672 + 1.99402i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(338\) −2.49236 + 3.96657i −2.49236 + 3.96657i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 2.88144 0.324660i 2.88144 0.324660i
\(347\) 0.867767 0.867767 0.433884 0.900969i \(-0.357143\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(348\) 0.580713 + 1.47963i 0.580713 + 1.47963i
\(349\) −1.46610 −1.46610 −0.733052 0.680173i \(-0.761905\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(350\) 0 0
\(351\) 1.92808 0.440071i 1.92808 0.440071i
\(352\) 0 0
\(353\) 0.702449 0.880843i 0.702449 0.880843i −0.294755 0.955573i \(-0.595238\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(354\) −0.334639 + 0.633168i −0.334639 + 0.633168i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −1.41476 + 2.25157i −1.41476 + 2.25157i
\(359\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(360\) 0 0
\(361\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(362\) 0 0
\(363\) 0.294755 + 0.955573i 0.294755 + 0.955573i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(368\) 0.0273204 0.0567315i 0.0273204 0.0567315i
\(369\) −1.19572 0.521689i −1.19572 0.521689i
\(370\) 0 0
\(371\) 0 0
\(372\) −0.212954 + 0.794755i −0.212954 + 0.794755i
\(373\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.0709414i 0.0709414i
\(377\) 0.722521 1.84095i 0.722521 1.84095i
\(378\) 0 0
\(379\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(380\) 0 0
\(381\) 1.58114 1.16694i 1.58114 1.16694i
\(382\) 0 0
\(383\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(384\) −1.54027 + 0.291435i −1.54027 + 0.291435i
\(385\) 0 0
\(386\) 1.35492 + 0.652497i 1.35492 + 0.652497i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.942673 0.106214i −0.942673 0.106214i
\(393\) −0.900198 0.774683i −0.900198 0.774683i
\(394\) −1.97085 + 1.97085i −1.97085 + 1.97085i
\(395\) 0 0
\(396\) 0 0
\(397\) −1.79690 0.865341i −1.79690 0.865341i −0.930874 0.365341i \(-0.880952\pi\)
−0.866025 0.500000i \(-0.833333\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.0392594 + 0.0492297i 0.0392594 + 0.0492297i
\(401\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(402\) 0 0
\(403\) 0.866803 0.544648i 0.866803 0.544648i
\(404\) −0.301381 2.67483i −0.301381 2.67483i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.694076 1.10462i −0.694076 1.10462i −0.988831 0.149042i \(-0.952381\pi\)
0.294755 0.955573i \(-0.404762\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −1.47493 0.643504i −1.47493 0.643504i
\(415\) 0 0
\(416\) 1.75820 + 1.10475i 1.75820 + 1.10475i
\(417\) 0.139129 + 1.85654i 0.139129 + 1.85654i
\(418\) 0 0
\(419\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(420\) 0 0
\(421\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(422\) 0.987409 + 2.05038i 0.987409 + 2.05038i
\(423\) −0.0747301 + 0.00279620i −0.0747301 + 0.00279620i
\(424\) 0 0
\(425\) 0 0
\(426\) 2.99382 + 0.112021i 2.99382 + 0.112021i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(432\) −0.0140115 0.0613885i −0.0140115 0.0613885i
\(433\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 1.60289 2.35100i 1.60289 2.35100i
\(439\) 1.94440 0.443797i 1.94440 0.443797i 0.955573 0.294755i \(-0.0952381\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(440\) 0 0
\(441\) 0.0747301 0.997204i 0.0747301 0.997204i
\(442\) 0 0
\(443\) −0.882094 + 0.308658i −0.882094 + 0.308658i −0.733052 0.680173i \(-0.761905\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −2.73695 0.957700i −2.73695 0.957700i
\(447\) 0 0
\(448\) 0 0
\(449\) −0.222521 + 1.97493i −0.222521 + 1.97493i 1.00000i \(0.5\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(450\) 1.21972 1.04966i 1.21972 1.04966i
\(451\) 0 0
\(452\) 0 0
\(453\) 0.997204 0.0747301i 0.997204 0.0747301i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −0.197822 0.314832i −0.197822 0.314832i 0.733052 0.680173i \(-0.238095\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(462\) 0 0
\(463\) 1.24698i 1.24698i −0.781831 0.623490i \(-0.785714\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(464\) −0.0586145 0.0230045i −0.0586145 0.0230045i
\(465\) 0 0
\(466\) 0.0269287 + 0.238998i 0.0269287 + 0.238998i
\(467\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(468\) 1.57176 2.72236i 1.57176 2.72236i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.139438 + 0.398492i 0.139438 + 0.398492i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 3.18921 + 0.359338i 3.18921 + 0.359338i
\(479\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1.43210 + 0.689663i 1.43210 + 0.689663i
\(485\) 0 0
\(486\) −1.55436 + 0.416490i −1.55436 + 0.416490i
\(487\) 0.702449 + 0.880843i 0.702449 + 0.880843i 0.997204 0.0747301i \(-0.0238095\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(488\) 0 0
\(489\) 0.0444073 + 0.0601697i 0.0444073 + 0.0601697i
\(490\) 0 0
\(491\) 0.169732 + 1.50641i 0.169732 + 1.50641i 0.733052 + 0.680173i \(0.238095\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(492\) −1.90062 + 0.829230i −1.90062 + 0.829230i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −0.0173412 0.0275983i −0.0173412 0.0275983i
\(497\) 0 0
\(498\) 0 0
\(499\) −1.14625 + 0.914101i −1.14625 + 0.914101i −0.997204 0.0747301i \(-0.976190\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(500\) 0 0
\(501\) −0.914101 + 0.848162i −0.914101 + 0.848162i
\(502\) 0 0
\(503\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −2.78181 + 0.858075i −2.78181 + 0.858075i
\(508\) 0.349732 3.10396i 0.349732 3.10396i
\(509\) 0.255779 + 0.531130i 0.255779 + 0.531130i 0.988831 0.149042i \(-0.0476190\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.0669543 0.106557i 0.0669543 0.106557i
\(513\) 0 0
\(514\) −2.06622 + 0.723001i −2.06622 + 0.723001i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 1.48883 + 1.01507i 1.48883 + 1.01507i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −0.531484 + 1.51889i −0.531484 + 1.51889i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) −1.87590 + 0.211363i −1.87590 + 0.211363i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.222521 0.974928i 0.222521 0.974928i
\(530\) 0 0
\(531\) −0.414278 + 0.162592i −0.414278 + 0.162592i
\(532\) 0 0
\(533\) 2.43523 + 0.852122i 2.43523 + 0.852122i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1.57906 + 0.487076i −1.57906 + 0.487076i
\(538\) 2.84912 1.37206i 2.84912 1.37206i
\(539\) 0 0
\(540\) 0 0
\(541\) −1.69226 1.06332i −1.69226 1.06332i −0.866025 0.500000i \(-0.833333\pi\)
−0.826239 0.563320i \(-0.809524\pi\)
\(542\) 1.38763 2.88144i 1.38763 2.88144i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.0332580 + 0.145713i 0.0332580 + 0.145713i 0.988831 0.149042i \(-0.0476190\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) −0.869485 + 0.379353i −0.869485 + 0.379353i
\(553\) 0 0
\(554\) −0.995587 + 0.625569i −0.995587 + 0.625569i
\(555\) 0 0
\(556\) 2.31365 + 1.84507i 2.31365 + 1.84507i
\(557\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(558\) −0.688241 + 0.469235i −0.688241 + 0.469235i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(564\) −0.0775357 + 0.0900981i −0.0775357 + 0.0900981i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 1.24884 1.24884i 1.24884 1.24884i
\(569\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(570\) 0 0
\(571\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(576\) −1.40870 0.813315i −1.40870 0.813315i
\(577\) 0.314832 0.197822i 0.314832 0.197822i −0.365341 0.930874i \(-0.619048\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(578\) 0.180173 + 1.59908i 0.180173 + 1.59908i
\(579\) 0.373714 + 0.856562i 0.373714 + 0.856562i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −0.373259 1.63535i −0.373259 1.63535i
\(585\) 0 0
\(586\) 0 0
\(587\) 1.09839 + 0.250701i 1.09839 + 0.250701i 0.733052 0.680173i \(-0.238095\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(588\) −1.08114 1.16519i −1.08114 1.16519i
\(589\) 0 0
\(590\) 0 0
\(591\) −1.72721 + 0.129436i −1.72721 + 0.129436i
\(592\) 0 0
\(593\) 0.781831 0.376510i 0.781831 0.376510i 1.00000i \(-0.5\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 3.00386 + 1.05109i 3.00386 + 1.05109i
\(599\) −1.05737 + 1.68280i −1.05737 + 1.68280i −0.433884 + 0.900969i \(0.642857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(600\) 0.0354707 0.947974i 0.0354707 0.947974i
\(601\) −1.82344 + 0.638050i −1.82344 + 0.638050i −0.826239 + 0.563320i \(0.809524\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.991043 1.24273i 0.991043 1.24273i
\(605\) 0 0
\(606\) 1.53510 2.25157i 1.53510 2.25157i
\(607\) 1.87590 0.211363i 1.87590 0.211363i 0.900969 0.433884i \(-0.142857\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0.146964 0.0165589i 0.146964 0.0165589i
\(612\) 0 0
\(613\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(614\) −1.06759 + 1.33872i −1.06759 + 1.33872i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(618\) 0 0
\(619\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(620\) 0 0
\(621\) −0.433884 0.900969i −0.433884 0.900969i
\(622\) −1.27989 2.65773i −1.27989 2.65773i
\(623\) 0 0
\(624\) 0.0367052 + 0.118995i 0.0367052 + 0.118995i
\(625\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(632\) 0 0
\(633\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(634\) −0.0801844 0.351311i −0.0801844 0.351311i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.97766i 1.97766i
\(638\) 0 0
\(639\) 1.36476 + 1.26631i 1.36476 + 1.26631i
\(640\) 0 0
\(641\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(642\) 0 0
\(643\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.531130 0.255779i −0.531130 0.255779i 0.149042 0.988831i \(-0.452381\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(648\) −0.443269 + 0.838705i −0.443269 + 0.838705i
\(649\) 0 0
\(650\) −2.25033 + 2.25033i −2.25033 + 2.25033i
\(651\) 0 0
\(652\) 0.118120 + 0.0133089i 0.118120 + 0.0133089i
\(653\) −1.91970 0.216299i −1.91970 0.216299i −0.930874 0.365341i \(-0.880952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.0271309 0.0775357i 0.0271309 0.0775357i
\(657\) 1.70798 0.457652i 1.70798 0.457652i
\(658\) 0 0
\(659\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(660\) 0 0
\(661\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(662\) 0.467798 + 0.373057i 0.467798 + 0.373057i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.988831 0.149042i −0.988831 0.149042i
\(668\) 1.98209i 1.98209i
\(669\) −0.900969 1.56052i −0.900969 1.56052i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.880843 0.702449i 0.880843 0.702449i −0.0747301 0.997204i \(-0.523810\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(674\) 0 0
\(675\) 1.00000 1.00000
\(676\) −2.00771 + 4.16905i −2.00771 + 4.16905i
\(677\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.590232 1.22563i −0.590232 1.22563i −0.955573 0.294755i \(-0.904762\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.974928 1.22252i 0.974928 1.22252i 1.00000i \(-0.5\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(692\) 2.79239 0.637344i 2.79239 0.637344i
\(693\) 0 0
\(694\) 1.38763 0.156348i 1.38763 0.156348i
\(695\) 0 0
\(696\) 0.443269 + 0.838705i 0.443269 + 0.838705i
\(697\) 0 0
\(698\) −2.34441 + 0.264152i −2.34441 + 0.264152i
\(699\) −0.0841939 + 0.123490i −0.0841939 + 0.123490i
\(700\) 0 0
\(701\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(702\) 3.00386 1.05109i 3.00386 1.05109i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0.964566 1.53510i 0.964566 1.53510i
\(707\) 0 0
\(708\) −0.258442 + 0.658499i −0.258442 + 0.658499i
\(709\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.366025 0.366025i −0.366025 0.366025i
\(714\) 0 0
\(715\) 0 0
\(716\) −1.13965 + 2.36651i −1.13965 + 2.36651i
\(717\) 1.35654 + 1.46200i 1.35654 + 1.46200i
\(718\) 0 0
\(719\) 1.22252 0.974928i 1.22252 0.974928i 0.222521 0.974928i \(-0.428571\pi\)
1.00000 \(0\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.856144 + 1.36254i 0.856144 + 1.36254i
\(723\) 0 0
\(724\) 0 0
\(725\) 0.563320 0.826239i 0.563320 0.826239i
\(726\) 0.643504 + 1.47493i 0.643504 + 1.47493i
\(727\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(728\) 0 0
\(729\) −0.900969 0.433884i −0.900969 0.433884i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.346781 0.991043i 0.346781 0.991043i
\(737\) 0 0
\(738\) −2.00605 0.618784i −2.00605 0.618784i
\(739\) 1.29637 + 0.146066i 1.29637 + 0.146066i 0.733052 0.680173i \(-0.238095\pi\)
0.563320 + 0.826239i \(0.309524\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(744\) −0.0731873 + 0.485566i −0.0731873 + 0.485566i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(752\) −0.000527223 0.00467923i −0.000527223 0.00467923i
\(753\) 0 0
\(754\) 0.823677 3.07401i 0.823677 3.07401i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.712362 0.162592i −0.712362 0.162592i −0.149042 0.988831i \(-0.547619\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(762\) 2.31812 2.15090i 2.31812 2.15090i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.792981 0.381879i 0.792981 0.381879i
\(768\) −0.856144 + 0.264085i −0.856144 + 0.264085i
\(769\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(770\) 0 0
\(771\) −1.26631 0.496990i −1.26631 0.496990i
\(772\) 1.40210 + 0.490615i 1.40210 + 0.490615i
\(773\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(774\) 0 0
\(775\) 0.488590 0.170965i 0.488590 0.170965i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(784\) 0.0629672 0.0629672
\(785\) 0 0
\(786\) −1.57906 1.07659i −1.57906 1.07659i
\(787\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(788\) −1.71654 + 2.15247i −1.71654